We begin by introducing a fundamental relation in logic, the implication.
To do so, we first define what a logical statement is. A logical statement dependent on several variables, which we denote by , is a statement, which, dependent on what values take, is either true or false. For example, consider the statement
Then we will have that is true, and is false; indeed, , but certainly not .
With this in mind, we may define the implication.
Let , be logical statements dependent on . Saying that implies (written ) means that whenever is true for given , then is also true.